Let $f$ be a linear function for which $f(6)-f(2)=12$. What is $f(12)-f(2)?$
Since $f$ is a linear function, its slope is constant. Therefore

\[\frac{f(6) - f(2)}{6-2} = \frac{f(12) - f(2)}{12 - 2},\]so \[\frac{12}{4} =\frac{f(12) - f(2)}{10},\]and $f(12) - f(2) = \boxed{30}$.